If 4 points are indicated on a line and 5 points are

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If 4 points are indicated on a line and 5 points are [#permalink]

16 May 2012, 06:52

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Question Stats:

79% (01:55) correct

20% (00:24) wrong

based on 6 sessions

If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

A. 20
B. 30
C. 40
D. 70
E. 90

Tried doing a few options, but couldn't get it right and the answer provided left me more confused!

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Re: If 4 points are indicated on a line and 5 points are [#permalink]

16 May 2012, 07:58

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alexpavlos wrote:

Approach #1:
There are two types of triangles possible:
With two vertices on the line with 4 points and the third vertex on the line with 5 points --> C^2_4*C^1_5=30;
With two vertices on the line with 5 points and the third vertex on the line with 4 points --> C^2_5*C^1_4=40;

Total: 30+40=70.

Answer: D.

Approach #2:

All different 3 points out of total 4+5=9 points will create a triangle EXCEPT those 3 points which are collinear.
C^3_{9}-(C^3_4+C^3_5)=84-(4+10)=70 (where C^3_4 and C^3_4 are # of different 3 collinear points possible from the line with 4 points and the line with 5 points, respectively).

Answer: D.

Hope it's clear.
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Re: If 4 points are indicated on a line and 5 points are indicat [#permalink]

16 May 2012, 07:04

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say line A with 4 points and line B with 5 points. and triangle is PQR.
If P is on line A and QR on line B we can have 4C1*5C2=40 triangles.
If P is on line B and QR on line A we can have 4C2*5C1=30 triangles.
Total =70 triangles.

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Re: If 4 points are indicated on a line and 5 points are [#permalink]

29 Dec 2012, 01:27

Not that fun this question

I wonder how often I would see such a question on test day.

Solution:

* * * * * (line B)

* * * * (line A)

Choose 2 points from line A and a point from line B: = 4!/2!2! * 5!/1!4! = 30
Choose 1 point from line A and 2 points from line B: = 4!/1!3! * 5!/2!3! = 4 * 10 = 40

Combine possiblities: 30 + 40 = 70

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If 4 points are indicated on a line and 5 points are [#permalink]

18 Feb 2013, 12:30

If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line,how many triangles can be formed whose vertices are among the 9 points?
(A)20
(B)30
(C)40
(D)70
(E)90

Need explanation.............

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Re: If 4 points are indicated on a line and 5 points are [#permalink]

18 Feb 2013, 12:34

mun23 wrote:

If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line,how many triangles can be formed whose vertices are among the 9 points?
(A)20
(B)30
(C)40
(D)70
(E)90

Need explanation.............

Merging similar topics. Please refer to the solutions above.
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Re: If 4 points are indicated on a line and 5 points are [#permalink] 18 Feb 2013, 12:34

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If 4 points are indicated on a line and 5 points are

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If 4 points are indicated on a line and 5 points are

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